Population Model of Serum Creatinine as Time-Dependent Covariate in Neonates

Abstract

Serum creatinine (sCr) is a commonly measured biomarker to estimate glomerular filtration rate (GFR) and therefore widely used as a covariate in population pharmacokinetic models of renally excreted drugs. In neonates, sCr dynamically changes during the first few weeks after birth. Missing covariates are a common problem in pharmacokinetic modeling of neonates due to the limited availability of blood sampling in number and volume. The objective of this work is to develop a parsimonious population model describing time courses of sCr in neonates with the intent to be incorporated into pharmacokinetic models of various drugs where sCr values are sparse or missing. The data for model development consisted of sCr measurements in 1080 newborns with a gestational age of 24–42 weeks. The model is based on a pharmacokinetic model of sCr that involves GFR, backflow of creatinine from the renal tubules, and urinary flow. Gestational age is the only covariate explaining between-subject variability of sCr. The model adequately describes distinct features of the sCr time course such as a peak and decline to a plateau. For a neonate with a GA of 35 weeks, the typical value of sCr at birth was 0.584 mg/dL, the peak (0.794 mg/dL) occurred 2.3 days after birth, to reach a plateau of 0.255 mg/dL approximately after 24.7 days. Model simulations reveal that in neonates with a similar postnatal age, sCr decreases with increasing GA. In summary, our model is designed to be a part of full random effects pharmacokinetic models where sCr is a significant covariate.

Appendix. Derivation of the quasi-steady state Eq. (6)

Dividing Eqs. (3)–(4) by GFR₀, one can obtain the time scale for creatinine clearance V_p/GFR₀ that is equal to 0.3 days for a typical term neonate of BWT =2.5 kg. If the time scale for GFR(t) due to kidney maturation is several days or longer, the factor V_p/GFR₀ will be proportionally decreased, justifying the quasi-steady-state assumption Eq. (5). Consequently,

$$ 0=\frac{{\mathrm{k}}_{\mathrm{syn}}}{{\mathrm{GFR}}_0}-\frac{\mathrm{GFR}\left(\mathrm{t}\right)}{{\mathrm{GFR}}_0}\cdotp \mathrm{sCr}+\frac{\mathrm{Q}\left(\mathrm{t}\right)}{{\mathrm{GFR}}_0}\cdotp \mathrm{rtCr} $$

(16)

$$ 0=\frac{\mathrm{GFR}\left(\mathrm{t}\right)}{{\mathrm{GFR}}_0}\cdotp \mathrm{sCr}-\frac{\mathrm{Q}\left(\mathrm{t}\right)}{{\mathrm{GFR}}_0}\cdotp \mathrm{rtCr}-\frac{\mathrm{UF}}{{\mathrm{GFR}}_0}\cdotp \mathrm{rtCr} $$

(17)

One can add Eqs. (16) and (17) side by side and arrive at

$$ 0=\frac{{\mathrm{k}}_{\mathrm{syn}}}{{\mathrm{GFR}}_0}-\frac{\mathrm{UF}}{{\mathrm{GFR}}_0}\cdotp \mathrm{rtCr} $$

(18)

Hence

$$ \mathrm{rtCr}=\frac{{\mathrm{k}}_{\mathrm{syn}}}{\mathrm{UF}} $$

(19)

On the other hand, solving Eq. (17) for yields

$$ \mathrm{sCr}=\left(\mathrm{UF}+\mathrm{Q}\left(\mathrm{t}\right)\right)\frac{\mathrm{rtCr}}{\mathrm{GFR}\left(\mathrm{t}\right)} $$

(20)

Substituting rtCr from Eq. (19) into Eq. (20) results in Eq. (6).